Identification of the piezoelectric material coefficients using the finite element method with an asymptotic waveform evaluation

A rapid identification of the piezoelectric material constants for a piezoelectric transducer is proposed. The validity of a three-dimensional finite element routine was confirmed experimentally. The asymptotic waveform evaluation (AWE) was adopted for a fast frequency sweep of the finite element analysis. The three-dimensional finite element method with an AWE and a design sensitivity method was used for a material inversion scheme of piezoelectric transducers. In order to confirm the inversion routine of the material constants, the mechanical displacements, which mean the mode shape, were calculated along the vertical and lateral position of the sample transducer.     

Identification of the piezoelectric material coefficients using the finite element method with an asymptotic waveform evaluation

A rapid identification of the piezoelectric material constants for a piezoelectric transducer is proposed. The validity of a three-dimensional finite element routine was confirmed experimentally. The asymptotic waveform evaluation (AWE) was adopted for a fast frequency sweep of the finite element analysis. The three-dimensional finite element method with an AWE and a design sensitivity method was used for a material inversion scheme of piezoelectric transducers. In order to confirm the inversion routine of the material constants, the mechanical displacements, which mean the mode shape, were calculated along the vertical and lateral position of the sample transducer.     

A single plate ultrasonic gyroscope in plane motion

We have proposed a vibration gyroscope made of a single piezoelectric plate in plane motion. The gyroscope makes use of the degenerated modes associated with a square plate. In the present paper, the experimental verification using an enlarged piezoelectric ceramic plate is presented, whose results are compared with the numerical prediction based on two-dimensional and three-dimensional finite element modelling.     

FINITE ELEMENT MODELLING OF LAMINATED PIEZO-ELASTIC STRUCTURES: LYAPUNOV STABILITY ANALYSIS

In this study, the dynamic stability of finite element modelling of laminated piezo-elastic structures is investigated. The criteria for stability are established based on the second method of Lyapunov, which considers the energy of the system. The results show that the equations of motion are asymptotically stable. However, energy dissipation through the piezoelectric effect continued at zero feedback gain. This implied that the structure was controlled unconditionally. Subsequently, a control strategy that satisfies the condition of no piezoelectric effects when the gain set to zero is developed.     

Active vibration control for structural-acoustic coupling system of a 3-D vehicle cabin model

This paper presents an active vibration control system for use with structural-acoustic coupling system using piezoelectric actuators and piezoelectric sensors. For modelling a complicated 3-D vehicle cabin model, the structural-acoustic coupling system is analyzed by combining the structural data from modal testing with the acoustic data from the finite element method. Through the structural-acoustic analysis program, the control plate and the control modes are selected, which are most effective for attenuating its noise. A robust LQG controller with two sensor signal filters is designed to remove the experimental problems such as the spillover effect due to uncontrolled modes. The robust LQG controller for the structural-acoustic coupling system can reduce the interior noise of the cavity as well as the structural vibration of the cabin.     

Analysis on vibration characteristics of large-size rectangular piezoelectric composite plate based on quasi-periodic phononic crystal structure

Based on the theory of composite materials and phononic crystals (PCs), a large-size rectangular piezoelectric composite plate with the quasi-periodic PC structure composed of PZT-4 and epoxy is proposed in this paper. This PC structure can suppress the transverse vibration of the piezoelectric composite plate so that the thickness mode is purer and the thickness vibration amplitude is more uniform. Firstly, the vibration of the model is analyzed theoretically, the electromechanical equivalent circuit diagram of three-dimensional coupled vibration is established, and the resonance frequency equation is derived. The effects of the length, width, and thickness of the piezoelectric composite plate at the resonant frequency are obtained by the analytical method and the finite element method, the effective electromechanical coupling coefficient is also analyzed. The results show that the resonant frequency can be changed regularly and the electromechanical conversion can be improved by adjusting the size of the rectangular piezoelectric plate. The effect of the volume fraction of the scatterer on the resonant frequency in the thickness direction is studied by the finite element method. The band gap in X and Y directions of large-size rectangular piezoelectric plate with quasi-periodic PC structures are calculated. The results show that the theoretical results are in good agreement with the simulation results. When the resonance frequency is in the band gap, the decoupling phenomenon occurs, and then the vibration mode in the thickness direction is purer.     

Strain distributions and electronic structure of three-dimensional InAs/GaAs quantum rings

This paper presents a finite element calculation for the electronic structure and strain distribution of self-organized InAs/GaAs quantum rings. The strain distribution calculations are based on the continuum elastic theory. An ideal three-dimensional circular quantum ring model is adopted in this work. The electron and heavy-hole energy levels of the InAs/GaAs quantum rings are calculated by solving the three-dimensional effective mass Schr?dinger equation including the deformation potential and piezoelectric potential up to the second order induced by the strain. The calculated results show the importance of strain and piezoelectric effects, and these effects should be taken into consideration in analysis of the optoelectronic characteristics of strain quantum rings.     

A modified axisymmetric finite element for the 3-D vibration analysis of piezoelectric laminated circular and annular plates

A finite element is presented to analyze the three-dimensional (3-D) vibration of piezoelectric coupled circular and annular plates. The proposed finite element is a modification of a conventional axisymmetric finite element and is capable of conducting both axisymmetric and nonaxisymmetric vibration analysis of circular and annular laminated plates, with piezoelectric layers therein. The present formulation, a two-dimensional model itself, can investigate 3-D vibration of those plates for a preselected number of nodal diameters, and is therefore more economical than the conventional 3-D finite element analysis, yet still has almost the same accuracy and versatility as the 3-D analysis. In cases such as analysis of stators of traveling wave ultrasonic motors where only vibration modes with particular numbers of nodal diameters are of interest, the proposed approach is very convenient and useful.     

Estimation of the loss factor of viscoelastic laminated panels from finite element analysis

A wave finite element (WFE) method is applied for predicting wave dispersion, wave attenuation and dissipation in viscoelastic laminated panels. The method involves postprocessing (using periodic structure theory) of element matrices of a small segment of the structure, which is modelled using a stack of three-dimensional finite elements meshed through the cross-section. Each layer can be discretised using either one solid element or more solid elements in order to more accurately represent interlaminar stress and strain. The finite element model of the segment of the structure is typically very small, resulting in very small computation cost. Formulations for the evaluation of the global loss factor using the WFE approach are given. In particular a formulation to calculate the average loss factor in the general case of an anisotropic component is proposed. Numerical examples are then shown. These concern the evaluation of the dispersion curves and of the global loss factor for damped laminated panels of different constructions.     

Ribs effects in acoustic radiation of a gearbox — their modelling in a boundary element method

Boundary element methods are nowadays currently used for acoustic radiation prediction of complex mechanic structures. Many of those structures contain an important account of ribs. The present paper deals with the acoustic influence of ribs and their modelling in a boundary element method. The influence of ribs is theoreticaly discussed and three different physical effects are distinguished : the “vibrating”, the “obstacle” and the ”source” effects. Further the modelling of ribs in boundary element meshes is discussed. An application to an automotive gearbox housing is then proposed. The vibrating behaviour of the structure is calculated with a finite element model, which has been updated thanks to an experimental modal analysis. The boundary element modelling necessity and the acoustic effects of the different ribs of the gearbox housing are studied.     

Estimating ensemble average power delivered by a piezoelectric patch actuator to a non-deterministic subsystem

Engineering systems such as aircraft, ships and automotive are considered built-up structures. Dynamically they are taught of as being fabricated from many components that are classified as ‘deterministic subsystems’ (DS) and ‘non-deterministic subsystems’ (Non-DS). Structures' response of the DS is deterministic in nature and analysed using deterministic modelling methods such as finite element (FE) method. The response of Non-DS is statistical in nature and estimated using statistical modelling technique such as statistical energy analysis (SEA). SEA method uses power balance equation, in which any external input to the subsystem must be represented in terms of power. Often, input force is taken as point force and ensemble average power delivered by point force is already well-established. However, the external input can also be applied in the form of moments exerted by a piezoelectric (PZT) patch actuator. In order to be able to apply SEA method for input moments, a mathematical representation for moment generated by PZT patch in the form of average power is needed, which is attempted in this paper. A simply-supported plate with attached PZT patch is taken as a benchmark model. Analytical solution to estimate average power is derived using mobility approach. Ensemble average of power given by the PZT patch actuator to the benchmark model when subjected to structural uncertainties is also simulated using Lagrangian method and FEA software. The analytical estimation is compared with the Lagrangian model and FE method for validation. The effects of size and location of the PZT actuators on the power delivered to the plate are later investigated.     

Piezoelectric effects and electronic structures of InAs/GaAs quantum dots grown along (111) and (011) directions

Piezoelectric effects and electronic structures of InAs/GaAs quantum dots grown along (111) and (011) directions are investigated in this paper. The finite element method is used. Electronic energy levels are calculated by solving the three-dimensional effective mass Schr?dinger equation including a strain modified confinement potential and piezoelectric effects. The difference in electronic structure between quantum dots grown along the (111) direction and the (011) direction are compared. The cubic and truncated pyramidal shaped quantum dots are adopted.     

Finite element modelling of piezolaminated smart structures for active vibration control with distributed sensors and actuators

Finite element modelling of laminated structures with distributed piezoelectric sensor and actuator layers and control electronics is considered in this paper. Beam, plate and shell type elements have been developed incorporating the stiffness, mass and electromechanical coupling effects of the piezoelectric laminates. The effects of temperature on the electrical and mechanical properties and the coupling between them are also taken into consideration in the finite element formulation. The piezoelectric beam element is based on Timoshenko beam theory. The plate/shell element is a nine-noded field-consistent element based on first order shear deformation theory. Constant-gain negative velocity feedback, Lyapunov feedback as well as a linear quadratic regulator (LQR) approach have been used for active vibration control with the structures subjected to impact, harmonic and random excitations. The influence of the pyroelectric effects on the vibration control performance is also investigated. The LQR approach is found to be more effective in vibration control with lesser peak voltages applied in the piezo actuator layers as in this case the control gains are obtained by minimizing a performance index. The application of these elements in high-performance, light-weight structural systems is highlighted.     

Finite element modeling of heating phenomena of cracks excited by high-intensity ultrasonic pulses

A three-dimensional thermo-mechanical coupled finite element model is built up to simulate the phenomena of dynamical contact and frictional heating of crack faces when the plate containing the crack is excited by high-intensity ultrasonic pulses.In the finite element model,the high-power ultrasonic transducer is modeled by using a piezoelectric thermal-analogy method,and the dynamical interaction between both crack faces is modeled using a contact-impact theory.In the simulations,the frictional heating taking place at the crack faces is quantitatively calculated by using finite element thermal-structural coupling analysis,especially,the influences of acoustic chaos to plate vibration and crack heating are calculated and analysed in detail.Meanwhile,the related ultrasonic infrared images are also obtained experimentally,and the theoretical simulation results are in agreement with that of the experiments.The results show that,by using the theoretical method,a good simulation of dynamic interaction and friction heating process of the crack faces under non-chaotic or chaotic sound excitation can be obtained.     

Analysis of a disk-type stator for the piezoelectric ultrasonic motor using impedance matrix

Impedance and admittance matrices of a piezoelectric annular actuator with segmented electrodes are presented for the analysis of the disk-type piezoelectric ultrasonic motors (USM). Equations of motion and the conjugate parameters for the impedance and admittance matrices are derived using the variational principle. In the derivation, the electric field in the piezoelectric layer is assumed to be constant over the area covered by a particular electrode, and the effects of both shear deformation and rotary inertia are taken into account. The resonance and antiresonance frequencies and the vibrating modes are calculated for the various resonance modes and boundary conditions, and the results are compared with those by the three-dimensional finite element methods. They are in excellent agreement with each other. It is expected that the derived impedance matrix can be effectively applied to the analysis and the design of the USM.     

三维电磁扩散场数值模拟及磁化效应的影响

采用矢量有限元法实现了三维电磁扩散场数值模拟,并成功将其应用在大地电磁的正演研究中.为灵活精确地拟合起伏地形和地下不规则构造,采用由不规则四面体单元组成的非结构化网格,可根据模型设计的需要调整网格的大小.引入了基于二次场理论,将解析的一次场从总场中扣除,直接计算二次场,使得误差仅局限于相对较小的二次场,以提高总场计算精度.常规的节点有限元法不满足电性分界面上法向电场不连续和无源区单元内电流密度无散,违反麦克斯韦方程组.为克服节点有限元法的弊端,使用矢量有限元法求解基于二次电场的偏微分方程.另外,在算法设计中,考虑了磁导率参数的变化,可以模拟磁导率不均匀的模型.通过与COMMEMI模型已发表的结果对比,证明了本文算法的正确性和精确性.为突显非结构网格优势,计算了椭球异常体模型和任意地形模型的MT响应,并详细讨论了地形和磁化效应对三维数值模拟结果的影响.     

Modeling of lamb waves generated by integrated transducers in composite plates using a coupled finite element-normal modes expansion method

Thin piezoelectric transducers attached to or embedded within composite structures could be used for in situ structural health monitoring. For plate-shaped structures, the useful ultrasonic vibration modes are Lamb waves. Preliminary testing has already demonstrated the suitability and practical feasibility of such integrated transducers, but better control of the generation of Lamb modes seems to be necessary. Therefore, an original modeling approach has been developed, which can be used to design and optimize these "sensitive materials." This modeling technique allows the determination of the amplitude of each Lamb mode excited in a composite plate with surface-bonded or bulk-embedded piezoelectric elements. The method consists of a coupling of the finite element method (FEM) and the normal modes expansion method. The limited finite element mesh of the transducer and its vicinity enables the computation of the mechanical field created by the transducer, which is then introduced as a forcing function into the normal modes equations. The adequacy and accuracy of this modeling method have been numerically and experimentally verified.     

A general finite element model for numerical simulation of structure dynamics

A finite element model used to simulate the dynamics with continuum and discontinuum is presented. This new approach is conducted by constructing the general contact model. The conventional discrete element is treated as a standard finite element with one node in this new method. The one-node element has the same features as other finite elements, such as element stress and strain. Thus, a general finite element model that is consistent with the existed finite element model is set up. This new model is simple in mathematical concept and is straightforward to be combined into the existing standard finite element code. Numerical example demonstrates that this new approach is more effective to perform the dynamic process analysis in which the interactions among a large number of discrete bodies and continuum objects are included.     

密度矩阵重正化群的异构并行优化

密度矩阵重正化群方法（DMRG）在求解一维强关联格点模型的基态时可以获得较高的精度,在应用于二维或准二维问题时,要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略,可以同时发挥计算机中央处理器（CPU）和图形处理器（GPU）的计算性能.针对最耗时的哈密顿量对角化部分,实现了数据的分布式存储,并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例,测试了异构并行程序在不同DMRG保留状态数下的运行表现,并给出了相应的性能基准.应用于4腿梯子时,观测到了高温超导中常见的电荷密度条纹,此时保留状态数达到10⁴,使用的GPU显存小于12 GB.     

响应面法的杆式超声电机有限元模型修正

现有杆式超声电机的有限元模型大都采用连续复合材料的简化结构形式,忽略了实际超声电机各部件间的接触特性,导致计算结果与实验结果具有较大偏差。针对该问题,提出了一种采用响应面法的杆式超声电机有限元模型修正方法,来获得高精度的有限元模型。该方法考虑了超声电机螺栓预紧力及各部件接触界面的法向接触刚度和摩擦系数,筛选出显著影响电机工作模态的参数,建立响应面模型替代超声电机的有限元模型实现快速计算结构响应的目的,并以实验模态分析结果为目标对模型进行修正。修正结果表明,修正后的模型模态频率的平均误差由修正前的1.20%降到0.21%,模型精度得到明显改善,表明以响应面的有限元模型修正方法对杆式超声电机以及类似夹心式压电振子的设计具有应用价值。